Denmark uses the kroner as its currency. Before a trip to Denmark, Mia wants to exchange $1,700 for kroner.
A. Does bank A or Bank B have the better exchange rate? Explain.
B. How many more kroner would Mia get if she exchanged her $1,700 at the bank with the better exchange rate?

Answer:

a. Bank A

b. 8,670 Kroner

Step-by-step explanation:

a. The bank that will give Mia a better exchange rate is the Bank who's exchange rate is higher in value, that is has more units of Kroner per $1.

Let's find which Bank has the best exchange rate.

Using the pair, (100, 510),

Bank A exchange rate = [tex] \frac{510}{100} = 5.1 [/tex]

Bank A exchange rate is 5.1 kroner per dollar

Using the point, (10, 50) on the graph,

Bank B exchange rate = [tex] \frac{50}{10} = 5 [/tex]

Bank B exchange rate is 5.0 kroner per dollar.

✅Therefore, Bank A has a better exchange rate.

Mia will get more Kroner per each dollar she wants to exchange if she lots for Bank A.

b. If Mia exchanged her $1,700 at Bank A, she would get:

1,700 × 5.1 = 8,670 Kroner.

a) The bank A have the best exchange rate.

b) Mia will receive an addition of 1303,90 crowns with the better exchange rate.

a) Given the existence of linear relationship between the amount of dollars ([tex]x[/tex]) and the expected amount of crowns ([tex]y[/tex]), the exchange rate ([tex]r[/tex]) is represented by the slope of each line, which is determined by definition of secant line.  The greater the slope, the better the exchange rate.

Now we proceed the exchange rate for each bank:

Bank A

[tex]r_{A} = \frac{612-408}{120 - 80}[/tex]

[tex]r_{A} = 5.1\,\frac{DKC}{USD}[/tex]

Bank B

[tex]r_{B} = \frac{130 - 0}{30 - 0}[/tex]

[tex]r_{B} = 4.333\,\frac{DKC}{USD}[/tex]

The bank A have the best exchange rate.

b) The addition ([tex]\Delta y[/tex]), in crowns, is defined by the following formula:

[tex]\Delta y = (r_{A}-r_{B})\cdot x[/tex] (1)

If we know that [tex]r_{A} = 5.1\,\frac{DKC}{USD}[/tex], [tex]r_{B} = 4.333\,\frac{DKC}{USD}[/tex] and [tex]x = 1700\,USD[/tex], then the addition is:

[tex]\Delta y = (5.1-4.333)\cdot 1700[/tex]

[tex]\Delta y = 1303,90\,DKC[/tex]

Mia will receive an addition of 1303,90 crowns with the better exchange rate.

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